Forests in lower-income countries provide a global public good, carbon sequestration. REDD, "reduced emissions from deforestation and forest degradation" is a performance-based payment designed to align private incentives at the country level with the socially optimal level of forest loss. This review article focuses on the distributional implications of REDD, specifically on whom the burdens and benefits fall. First, REDD implementation has proven more difficult and costly than originally anticipated. The literature highlights many costs of REDD over and above the opportunity cost, including readiness, enforcement and monitoring, which initially were underestimated or ignored. Second, ensuring additionality, minimising leakage, and spatial targeting of carbon rich locations, are difficult and costly, and shown in the literature to sometimes be at odds with pro-poor efforts. Third, benefit sharing has emerged in the literature as a central element of REDD implementation. Rural households may use nearby forests yet have no rights, and REDD may bring no benefits whilst imposing costs on these communities. Where REDD is implemented at the community level, incentives may not be aligned at the level of the individual, reducing REDD's impact and increasing conflict. Finally, funding sources are closely linked to the incidence of benefits and burdens. Our review suggests that, over a decade on from the Paris Agreement, REDD continues to be controversial, with equity-efficiency trade-offs often difficult to avoid. However, the literature provides considerable theoretical and empirical evidence as to how and where REDD can have a positive impact on both carbon sequestration and livelihoods.